Theorems · Definition · nonassociative algebras

LieModule.maxTrivLinearMapEquivLieModuleHom

{R : Type u} →
  {L : Type v} →
    {M : Type w} →
      {N : Type w₁} →
        [inst : CommRing R] →
          [inst_1 : LieRing L] →
            [inst_2 : LieAlgebra R L] →
              [inst_3 : AddCommGroup M] →
                [inst_4 : Module R M] →
                  [inst_5 : LieRingModule L M] →
                    [inst_6 : LieModule R L M] →
                      [inst_7 : AddCommGroup N] →
                        [inst_8 : Module R N] →
                          [inst_9 : LieRingModule L N] →
                            [inst_10 : LieModule R L N] →
                              ↥(LieModule.maxTrivSubmodule R L (M →ₗ[R] N)) ≃ₗ[R] M →ₗ⁅R,L⁆ N

A linear map between two Lie modules is a morphism of Lie modules iff the Lie algebra action on it is trivial.

Defined in

Mathlib.Algebra.Lie.Abelian

Cited by

4 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleAddCommGroupModuleLieRingModuleLieModule